A gravitational-wave standard siren measurement of the 1 Hubble constant 2 B. Abbott 1 , M. Others 2 & E. M. Partners 3 3 1 LIGO 4 2 Virgo 5 3 Everywhere 6 P1700296-v3 7 September 29, 2017 8 We report the first determination of the Hubble constant, which is the local expansion rate 9 of the Universe, using gravitational wave measurements. The spiraling together of two com- 10 pact objects, such as neutron stars or black holes, is a “standard siren”: the waves emitted 11 tell us the distance to the binary. The observation by the LIGO and Virgo detectors of the 12 neutron-star merger event GW170817, combined with follow-up optical observations of the 13 post-merger explosion, allows us to measure both the distance and the recession velocity of 14 the standard siren’s host galaxy, NGC4993, and thereby infer the Hubble constant. Our 15 measured value is consistent with existing estimates, while being completely independent of 16 them. Future gravitational wave observations of merger events will enable more precise mea- 17 surements of the Hubble constant. 18 The detection of GW170817 1 heralds the age of multi-messenger astronomy, with the obser- 19 1
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A gravitational-wave standard siren measurement of the1
Hubble constant2
B. Abbott1, M. Others2 & E. M. Partners33
1LIGO4
2Virgo5
3Everywhere6
P1700296-v37
September 29, 20178
We report the first determination of the Hubble constant, which is the local expansion rate9
of the Universe, using gravitational wave measurements. The spiraling together of two com-10
pact objects, such as neutron stars or black holes, is a “standard siren”: the waves emitted11
tell us the distance to the binary. The observation by the LIGO and Virgo detectors of the12
neutron-star merger event GW170817, combined with follow-up optical observations of the13
post-merger explosion, allows us to measure both the distance and the recession velocity of14
the standard siren’s host galaxy, NGC 4993, and thereby infer the Hubble constant. Our15
measured value is consistent with existing estimates, while being completely independent of16
them. Future gravitational wave observations of merger events will enable more precise mea-17
surements of the Hubble constant.18
The detection of GW1708171 heralds the age of multi-messenger astronomy, with the obser-19
1
vations of gravitational-wave (GW) and electromagnetic (EM) emission from the same transient20
source. On 17 August 2017 the network of Advanced Laser Interferometer Gravitational-wave21
Observatory (LIGO)2 and Virgo3 detectors observed GW170817, a strong signal from the merger22
of a compact-object binary. The source was localized to a region of 28 deg2 (90% credible re-23
gion). Independently, the Fermi Gamma-Ray Burst Monitor (GBM)4 detected a weak Gamma Ray24
Burst (GRB) event GRB170817A consistent with the same sky region, less than 2 seconds after the25
compact binary merger5–7. The LIGO-Virgo localization region was subsequently observed by a26
number of optical astronomy facilities8, resulting in the identification of an optical transient signal27
within ∼ 10 arcsec of the galaxy NGC 4993 (Swope, DECam, DLT40 2017 in prep., Valenti et28
al. ApJL, accepted, LCOGT, VISTA, MASTER). GW170817 is therefore the first source to have29
been detected in both GWs and EM waves, and the first GW source with a known host galaxy. This30
event can therefore be used as a standard siren9–13 to determine the Hubble constant, combining the31
distance inferred purely from the GW signal with the Hubble flow velocity of the galaxy contain-32
ing the electromagnetic transient. Such measurements do not require any form of cosmic “distance33
ladder”14; the GW analysis directly estimates the luminosity distance out to cosmological scales.34
The Hubble constant H0 measures the mean expansion rate of the Universe. At nearby35
distances (d . 100 Mpc) it is well approximated by the expression36
vH = H0d, (1)
where vH is the local “Hubble flow” velocity of a source, and d is the distance to the source. At37
this nearby distance all cosmological distance measures (such as luminosity distance and comoving38
distance) differ by less than 1%, so we do not distinguish among them. We are similarly insensitive39
2
to the values of other cosmological parameters, such as Ωm and ΩΛ. An analysis of the GW40
data finds that GW170817 occurred at a distance d = 43.8+2.9−6.9 Mpc1. (All values are quoted as41
the maximum posterior value with the minimal width 68.3% credible interval). To obtain the42
Hubble flow velocity at the position of GW170817, we use the optical identification of the host43
galaxy NGC 49938. This identification is based solely on the 2-dimensional projected offset and44
is independent of any assumed value of H0. The position and redshift of this galaxy allow us to45
estimate the appropriate value of the Hubble flow velocity.46
The original standard siren proposal9 did not rely on the unique identification of a host galaxy.47
As long as a possible set of host galaxies can be identified for each GW detection, by combining48
information from ∼ 100 independent detections, an estimate of H0 with ∼ 5% uncertainty can be49
obtained event without the detection of any transient optical counterparts15. If an EM counterpart50
has been identified but the host galaxy is unknown, the same statistical method can be applied51
but using only those galaxies in a narrow beam around the location of the optical counterpart.52
However, such statistical analyses are sensitive to a number of complicating effects, including the53
incompleteness of current galaxy catalogs16 or the need for dedicated follow-up surveys, as well54
as a range of selection effects17. In what follows we exploit the identification of NGC 4993 as the55
host galaxy of GW170817 to perform a standard siren measurement of the Hubble constant10–13.56
The gravitational wave observation57
Analysis of the GW data associated with GW170817 produces estimates for the parameters of the58
1The distance quoted here differs from that in other studies1, since here we assume that the optical counterpart
represents the true sky position of the GW source instead of marginalizing over a range of potential sky positions.
3
source, under the assumption that General Relativity is the correct model of gravity. Parameters59
are inferred within a Bayesian framework18 by comparing strain measurements1 in the two LIGO60
detectors and the Virgo detector with the gravitational waveforms expected from the inspiral of two61
point masses19 under general relativity. We are most interested in the joint posterior distribution on62
the luminosity distance and binary orbital inclination angle. For the analysis in this paper we fix63
the location of the GW source on the sky to the identified location of the counterpart20. This anal-64
ysis uses algorithms for removing short-lived detector noise artifacts1, 21 and employs approximate65
point-particle waveform models19, 22, 23. We have verified that the systematic changes in the results66
presented here from incorporating non-point-mass (tidal) effects24, 25 and from different data pro-67
cessing methods are much smaller than the statistical uncertainties in the measurement of H0 and68
the binary orbital inclination angle.69
The distance to GW170817 is estimated from the GW data alone to be 43.8+2.9−6.9 Mpc. The70
∼ 15% uncertainty is due to a combination of statistical measurement error from the noise in71
the detectors, instrumental calibration uncertainties1, and a geometrical factor dependent upon the72
correlation of distance with inclination angle. The GW measurement is consistent with the distance73
to NGC 4993 measured using the Tully-Fisher relation, dTF = 41.1± 5.8 Mpc14, 26.74
The measurement of the GW polarization is crucial for inferring the binary inclination. This75
inclination, ι, is defined as the angle between the line of sight vector from the source to the detector76
and the angular momentum vector of the binary system. Observable electromagnetic phenomena77
cannot typically distinguish between face-on and face-off sources, and therefore are usually char-78
4
acterized by a viewing angle: min (ι, 180 deg−ι). By contrast, GW measurements can identify79
whether a source is rotating counter-clockwise or clockwise with respect to the line of sight, and80
thus ι ranges from 0 to 180 deg. Previous GW detections by LIGO had large uncertainties in lu-81
minosity distance and inclination27 because the two LIGO detectors that were involved are nearly82
co-aligned, preventing a precise polarization measurement. In the present case, thanks to Virgo as83
an additional detector, the cosine of the inclination can be constrained at 68.3% (1-σ) confidence84
to the range [−1,−0.81] corresponding to inclination angles between [144, 180] deg. This implies85
that the plane of the binary orbit is almost, but not quite, perpendicular to our line of sight to86
the source (ι ≈ 180 deg), which is consistent with the observation of a coincident GRB5–7 (LVC,87
GBM, INTEGRAL 2017 in prep., Goldstein et al. 2017, ApJL, submitted, and Savchenko et al.88
2017, ApJL, submitted).89
The electromagnetic observations90
EM follow-up of the GW sky localization region8 discovered an optical transient20, 28–31 in close91
proximity to the galaxy NGC 4993. The location of the transient was previously observed by the92
Hubble Space Telescope on 2017 April 28 UT and no sources were found within 2.2 arcseconds93
down to 25.9 mag32. We estimate the probability of a random chance association between the94
optical counterpart and NGC 4993 to be 0.004% (see the methods section for details). In what95
follows we assume that the optical counterpart is associated with GW170817, and that this source96
resides in NGC 4993.97
To compute H0 we need to estimate the background Hubble flow velocity at the position98
5
of NGC 4993. In the traditional electromagnetic calibration of the cosmic “distance ladder”14,99
this step is commonly carried out using secondary distance indicator information, such as the100
Tully-Fisher relation26, which allows one to infer the background Hubble flow velocity in the local101
Universe scaled back from more distant secondary indicators calibrated in quiet Hubble flow. We102
do not adopt this approach here, however, in order to preserve more fully the independence of our103
results from the electromagnetic distance ladder. Instead we estimate the Hubble flow velocity at104
the position of NGC 4993 by correcting for local peculiar motions.105
NGC 4993 is part of a collection of galaxies, ESO-508, whose center-of-mass recession ve-106
locity relative to our local CMB frame33 is34, 35 3327 ± 72 km s−1. We correct the group velocity107
by 310 km s−1 due to the coherent bulk flow36, 37 towards The Great Attractor (see Methods section108
for details). The standard error on our estimate of the peculiar velocity is 69 km s−1, but recogniz-109
ing that this value may be sensitive to details of the bulk flow motion that have been imperfectly110
modelled, in our subsequent analysis we adopt a more conservative estimate37 of 150km s−1 for111
the uncertainty on the peculiar velocity at the location of NGC 4993, and fold this into our estimate112
of the uncertainty on vH . From this, we obtain a Hubble velocity vH = 3024± 166 km s−1.113
Analysis114
Once the distance and Hubble velocity distributions have been determined from the GW and EM115
data, respectively, we can constrain the value of the Hubble constant. The measurement of the116
distance is strongly correlated with the measurement of the inclination of the orbital plane of the117
binary. The analysis of the GW data also depends on other parameters describing the source,118
6
such as the masses of the components18. Here we treat the uncertainty in these other variables119
by marginalizing over the posterior distribution on system parameters1, with the exception of the120
position of the system on the sky which is taken to be fixed at the location of the optical counterpart.121
We carry out a Bayesian analysis to infer a posterior distribution on H0 and inclination,122
marginalized over uncertainties in the recessional and peculiar velocities; see the Methods sec-123
tion for details. Figure 1 shows the marginal posterior for H0. The maximum a posteriori value124
with the minimal 68.3% credible interval is H0 = 70+12−8 km s−1 Mpc−1. Our estimate agrees well125
with state-of-the-art determinations of this quantity, including CMB measurements from Planck38126
(67.74 ± 0.46 km s−1 Mpc−1, “TT,TE,EE+lowP+lensing+ext”) and Type Ia supernova measure-127
ments from SHoES39 (73.24 ± 1.74 km s−1 Mpc−1), as well as baryon acoustic oscillations mea-128
surements from SDSS40, strong lensing measurements from H0LiCOW41, high-l CMB measure-129
ments from SPT42, and Cepheid measurements from the HST key project14. Our measurement is a130
new and independent determination of this quantity. The close agreement indicates that, although131
each method may be affected by different systematic uncertainties, we see no evidence at present132
for a systematic difference between GW and EM-based estimates. As has been much remarked133
upon, the Planck and SHoES results are inconsistent at & 3σ level. Our measurement does not134
resolve this tension, falling neatly between the two values and being broadly consistent with both.135